Finding Variable Pattern within Predefined Clusters

I have this unique situation where I have predefined clusters (based on certain attributes - that I cant get due to certain restrictions). For each record within each cluster I have a set of financial variable. These clusters were defined on some historical financial variables. So now I want a way where I can use accounts within each cluster to find attributes that lead to that account falling in a particular cluster. Basically come up with an algorithm where if I have an account, I can use its attributes to decide which cluster would it fall into.

Any info would be helpful.